TY - GEN
T1 - Obfuscation of probabilistic circuits and applications
AU - Canetti, Ran
AU - Lin, Huijia
AU - Tessaro, Stefano
AU - Vaikuntanathan, Vinod
N1 - Publisher Copyright:
© International Association for Cryptologic Research 2015.
PY - 2015
Y1 - 2015
N2 - This paper studies the question of how to define, construct, and use obfuscators for probabilistic programs. Such obfuscators compil a possibly randomized program into a deterministic one, which achieves computationally indistinguishable behavior from the original program as long as it is run on each input at most once. For obfuscation, we propose a notion that extends indistinguishability obfuscation to probabilistic circuits: It should be hard to distinguish between the obfuscations of any two circuits whose output distributions at each input are computationally indistinguishable, possibly in presence of some auxiliary input. We call the resulting notion probabilistic indistinguishability obfuscation (pIO). We define several variants of pIO, and study relations among them. Moreover, we give a construction of one of our variants, called X-pIO, from sub-exponentially hard indistinguishability obfuscation (for deterministic circuits) and one-way functions. We then move on to show a number of applications of pIO. In particular, we first give a general and natural methodology to achieve fully homomorphic encryption (FHE) from variants of pIO and of semantically secure encryption schemes. In particular, one instantiation leads to FHE from any X-pIO obfuscator and any re-randomizable encryption scheme that’s slightly super-polynomially secure. We note that this constitutes the first construction of full-fledged FHE that does not rely on encryption with circular security. Moreover, assuming sub-exponentially secure puncturable PRFs computable in NC1, sub-exponentially-secure indistinguishability obfuscation for (deterministic) NC1 circuits can be bootstrapped to obtain indistinguishability obfuscation for arbitrary (deterministic) poly-size circuits (previously such bootstrapping was known only assuming FHE with NC1 decryption algorithm).
AB - This paper studies the question of how to define, construct, and use obfuscators for probabilistic programs. Such obfuscators compil a possibly randomized program into a deterministic one, which achieves computationally indistinguishable behavior from the original program as long as it is run on each input at most once. For obfuscation, we propose a notion that extends indistinguishability obfuscation to probabilistic circuits: It should be hard to distinguish between the obfuscations of any two circuits whose output distributions at each input are computationally indistinguishable, possibly in presence of some auxiliary input. We call the resulting notion probabilistic indistinguishability obfuscation (pIO). We define several variants of pIO, and study relations among them. Moreover, we give a construction of one of our variants, called X-pIO, from sub-exponentially hard indistinguishability obfuscation (for deterministic circuits) and one-way functions. We then move on to show a number of applications of pIO. In particular, we first give a general and natural methodology to achieve fully homomorphic encryption (FHE) from variants of pIO and of semantically secure encryption schemes. In particular, one instantiation leads to FHE from any X-pIO obfuscator and any re-randomizable encryption scheme that’s slightly super-polynomially secure. We note that this constitutes the first construction of full-fledged FHE that does not rely on encryption with circular security. Moreover, assuming sub-exponentially secure puncturable PRFs computable in NC1, sub-exponentially-secure indistinguishability obfuscation for (deterministic) NC1 circuits can be bootstrapped to obtain indistinguishability obfuscation for arbitrary (deterministic) poly-size circuits (previously such bootstrapping was known only assuming FHE with NC1 decryption algorithm).
UR - http://www.scopus.com/inward/record.url?scp=84924401939&partnerID=8YFLogxK
U2 - 10.1007/978-3-662-46497-7_19
DO - 10.1007/978-3-662-46497-7_19
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AN - SCOPUS:84924401939
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 468
EP - 497
BT - Theory of Cryptography - 12th Theory of Cryptography Conference, TCC 2015, Proceedings
A2 - Dodis, Yevgeniy
A2 - Nielsen, Jesper Buus
PB - Springer Verlag
T2 - 12th Theory of Cryptography Conference, TCC 2015
Y2 - 23 March 2015 through 25 March 2015
ER -